I think it's a matter of size too. Mice are little and easy to chase. Squirrels are more imposing and usually too quick for a cat to catch. Same with birds. A cat would go for a robin or something, but not for say a crow or an eagle <img src="/images/graemlins/smile.gif" alt="" />
My cats are indoor cats and they catch little mice sometimes from the basement. But I imagine if they came up against a raccoon or something they'd be less eager to "play".